Is arc ABC equal in length to arc DEF ? (1) AD⊥CF (2) AD and CF bis

Question

https://gmatclub.com/forum/download/file.php?id=55569 Is arc ABC equal in length to arc DEF ? (1) AD ⊥ CF (2) AD and CF bisect each other. Are You Up For the Challenge: 700 Level Questions Project DS Butler Data Sufficiency (DS3) For DS butler Questions Click Here download.png

rajatchopra1994 · Answer

Explanation:

Statement 1: AD ⊥ CF 
When M is the center, ABC = FED
When M is not the center, ABC≠FED
Not Sufficient.

Statement 2: AD and CF bisect each other
Then M has to be at center, and both AD & CF will dia of circle.
Sufficient.

IMO-B

yashikaaggarwal · Answer

To find: Is arc ABC equal in length to arc DEF ?

Solution: for this AM=CM=DM=FM ( Practically AD and CF to be diameters) so that they subtend equal arc
(1) AD ⊥ CF
No idea whether AD and CF are of equal length. Chords can also be perpendicular but won't subtend equal arc, or they can be diameters, which will subtend equal arc. ( INSUFFICIENT )

(2) AD and CF bisect each other.
So, AD And CF are divided into four equal parts, making AM=CM=DM=FM, ( only possible in diameter)
Hence they subtend equal arc ( Sufficient)

IMO B

GMATinsight · Answer

Question: Is arc ABC equal in length to arc DEF ?

Statement 1 :AD ⊥ CF

Two perpendicular lines do not always have opposite arc lengths equal UNLESS THEY INTERSECT AT CENTER OF CIRCLE (which is not confirmed) hence

NOT SUFFICIENT

Statement 2 : AD and CF bisect each other

CONCEPT:  Two chord bisect in a circle only if they intersect at center of the circle

Now, since the chords are bisecting therefore their opposite arcs must eb equal hence

SUFFICIENT

Answer: Option B

TestPrepUnlimited · Answer

In order for the arcs to have equal length, we need to have M be the center of the circle.

Statement 1 does not guarantee M is in the center, insufficient.

Statement 2 tells us M is the middle point of AD and CF, this can only be the case if both AD and CF are diameters of the circle. Thus M is the center of the circle, sufficient.

sambitspm · Answer

Kindly see the attachment.

There is nowhere mentioned that AD and CF are chords. So I didn't assume that they can become diameters in Option B. 
AM, MD, CM, MF all can be radii.

IMO C

Is arc ABC equal in length to arc DEF ? (1) AD⊥CF (2) AD and CF bis

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards